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On There Being Infinitely Many Thinkable Thoughts: A Reply to Porpora and a Defence of Tegmark

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Abstract

Porpora (2013) offers an a priori argument for the conclusion that there are infinitely many thoughts that it is physically possible for us to think. That there should be such an a priori argument is astonishing enough. That the argument should be simple enough to teach to a first-year undergraduate class in about 20 min, as Porpora’s is, is more astonishing still. Porpora’s main target is Max Tegmark’s recent argument for the claim that if current physics is right, then there are mental duplicates of us in far flung regions of the Universe. His argument is directed against Tegmark’s assumption that mental facts supervene upon physical facts. So, if Porpora’s argument is sound then not only is Tegmark’s argument unsound, but physicalism is also false. So, Porpora’s argument is powerful indeed. Who would have thought that a simple a priori argument, together with the physical facts, could solve the issue of whether physicalism is true?. Not I. In this paper I take a closer look at Porpora’s argument and show that it is fallacious. I also consider the other reasons Porpora gives for thinking there are infinitely many thinkable thoughts and find them similarly lacking.

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Notes

  1. According to Tegmark each of us would likely find a duplicate of ourselves about \( {10}^{10^{115}} \) m away. (Tegmark 2009)

  2. See Tegmark (2003, 2009). Porpora notes that Tegmark’s calculation that each of us would likely find a duplicate of ourselves about \( {10}^{10^{115}} \) m away rests on the assumption that each combination of quantum states in a Hubble volume has an equal chance of occurring. This is true. But his general argument given here for the conclusion that there are Hubble volumes that contain mental duplicates of us does not. All it requires is that each combination of quantum states has a non-zero probability of occurring.

  3. Physicalism can be cashed out in a variety of ways, but that the mental supervenes on the physical is a common commitment of all physicalists. See Lewis (1983: 361). So although Porpora says that his argument is directed specifically at Humean supervenience (Porpora 2013: 135), if sound it refutes any physicalist view.

  4. Indeed, throughout his paper Porpora often formulates the question of whether we can think about numbers directly in terms of whether we can refer to them. See, e.g. (Porpora 2013: 144).

  5. There are a variety of diagnoses of precisely what the semantic defect consists in. See, for example Chihara (1979, 1984), Grover (1983), French (1988). But everyone agrees that Berry’s paradox requires resolution and that the semantically-involved description within it is defective.

  6. The modified argument runs as follows:

    1. Let us stipulate that what any of us on Earth thinks (explicitly or implicitly) at any point in time is a subset of a larger set of all thoughts that will be thought at some time on Earth (or of mental states that someone on Earth will be in at some time). Suppose this larger set consists of only finitely many thoughts (or mental states).

    2. If we will think only finitely many thoughts (on Earth), then there are only finitely many integers of which we will think (on Earth).

    3. If there are only finitely many integers of which we will think (on Earth), then there must be some integer that is the largest that we will think of (on Earth). Call this largest integer ‘N’.

    4. But we are now thinking of N, and so can now think of N + 1 or 2 N or N2 and so on, all larger than N, which, therefore, cannot be the largest integer that we will think of (on Earth), contradicting the conclusion of the previous step.

    5. So there is no integer that is the largest we will think of (on Earth).

    6. Then there are not only finitely many integers of which we will think (on Earth).

    7. Then the larger set of all thoughts that we will think (on Earth) must be infinite.

  7. For a classic argument for the existence of wide contents see Putnam (1975). For what it’s worth, I think it is implausible that descriptions such as these do have wide content. Even neo-Russellians are apt to deny this and maintain that we can only entertain singular thoughts if we are in some sense acquainted with the object we are thinking of (even if this is an indirect causal acquaintance). But as we will see, even if descriptions like the ones mentioned here do not have wide content, this will not save Porpora. Whether they do or not, thoughts must be individuated by narrow content in the argument he gives. Supposing that descriptions like the ones mentioned do have wide contents helps to see why.

  8. One might alternatively say that an implicit belief is a proposition that is entailed by our occurrent beliefs and is such that we would assent to it were it logically possible for us to entertain it. But this is no help to Porpora. Then the only conclusion we could then draw from the argument he gives is that there are infinitely many thoughts that it is logically possible for us to think, and this has no bearing on how many thoughts it is physically possible for us to think.

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  1. Lecturer in Philosophy, School of English Culture and Media, Nottingham Trent University, Nottingham, NG11 8NS, UK

    Benjamin L. Curtis

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  1. Benjamin L. Curtis
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Curtis, B.L. On There Being Infinitely Many Thinkable Thoughts: A Reply to Porpora and a Defence of Tegmark. Philosophia 43, 35–42 (2015). https://doi.org/10.1007/s11406-014-9560-8

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